Pricing of Credit Derivatives with and without Counterparty and Collateral Adjustments

Alexander Lipton and David Shelton

Contents

Introduction to 'Lessons from the Financial Crisis'

1.

The Credit Crunch of 2007: What Went Wrong? Why? What Lessons Can be Learned?

2.

Underwriting versus Economy: A New Approach to Decomposing Mortgage Losses

3.

The Shadow Banking System and Hyman Minsky’s Economic Journey

4.

The Collapse of the Icelandic Banking System

5.

The Quant Crunch Experience and the Future of Quantitative Investing

6.

No Margin for Error: The Impact of the Credit Crisis on Derivatives Markets

7.

The Re-Emergence of Distressed Exchanges in Corporate Restructurings

8.

Modelling Systemic and Sovereign Risks

9.

Measuring and Managing Risk in Innovative Financial Instruments

10.

Forecasting Extreme Risk of Equity Portfolios with Fundamental Factors

11.

Limits of Implied Credit Correlation Metrics Before and During the Crisis

12.

Another view on the pricing of MBSs, CMOs and CDOs of ABS

13.

Pricing of Credit Derivatives with and without Counterparty and Collateral Adjustments

14.

A Practical Guide to Monte Carlo CVA

15.

The Endogenous Dynamics of Markets: Price Impact, Feedback Loops and Instabilities

16.

Market Panics: Correlation Dynamics, Dispersion and Tails

17.

Financial Complexity and Systemic Stability in Trading Markets

18.

The Martingale Theory of Bubbles: Implications for the Valuation of Derivatives and Detecting Bubbles

19.

Managing through a Crisis: Practical Insights and Lessons Learned for Quantitatively Managed Equity Portfolios

20.

Active Risk Management: A Credit Investor’s Perspective

21.

Investment Strategy Returns: Volatility, Asymmetry, Fat Tails and the Nature of Alpha

Subsequent to the financial crisis of 2007–8, the credit value adjustment (CVA) for derivatives positions (that is, the adjustment to valuation required to account for the credit risk of one or both counter-parties who have entered into a portfolio of transactions) has been an area of heightened focus for banks, regulators and politicians.

In this chapter we will concentrate on the particular case of a portfolio of single name credit default swaps (CDSs). This is a pertinent example since it exhibits so-called “wrong way risk” (Redon 2006); in other words, the size of the exposure is positively correlated with the likelihood of default of the counterparty, as well as being highly asymmetric with respect to the two counterparties. In order to capture this effect, we need to model the default correlation between issuers with a common factor. As we will see, in order to generate significant default correlation it becomes essential to incorporate jumps in this process, representing sudden economy-wide deterioration of credit quality.

Whatever the underlying political motivation for attempting to introduce one or more central clearing counterparties for CDSs, it is clear (Duffie

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